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What are back edges for in Ford-Fulkerson algorithm?

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Borrowing a good example from topcoder post- Maximum Flow: Section 1. The image below shows the chosen path : X -> B -> C -> Y with flow=1. We add the back edges correspondingly for the path. read more

Back edges are the edges on which you can decrease the flow to find new paths which can potentially lead to a higher flow than the current value. This can happen in cases when you pick a path which prevent other paths from being picked which might result in higher flow. read more

The given graph is directed and there is an edge from A to B with capacity y. Now sending a flow of x units (x < y) from A to B is equivalent to sending -x units from B to A, so we add a back edge from B to A of capacity x units. And the FF algorithm can send a flow of x units from B to A in the future. read more

As an example where back edges are necessary, consider this flow network: s / \ a b \ / \ c d \ / t Assume that all edges point down and that all edges have capacity 1 and that you want to find a flow from s to t. Suppose on the first iteration of Ford-Fulkerson that you take the path s -> b -> c -> t. read more

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